Most of the time, when you have a simple SDE without a drift, it's a martingale because the Wiener process itself is a martingale. In your example, you have a constant with the Wiener process, therefore the whole process must also be a martingale because the expectation is clearly X(t).

However, we can't conclude a driftless SDE is always a martingale. There're cases that a driftless SDE is a local-martingale or super-martingale. What we can conclude in your example that it's an obvious martingale.